Answers
➝ Hypotenuse of triangle ( a ) = 21.63 mm
➝ Hypotenuse of triangle ( b ) = 150 mm
➝ Hypotenuse of triangle ( c ) = 111.80 mm
[tex] \quad\rule{300pt}{1.5pt}\quad[/tex]
Solution:We have to find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
Pythagoras theorem states that :" In a right angled triangle, the square of hypotenuse side is equal to the sum of square of other two sides "
[tex] \qquad \bull \:{\pmb{\mathfrak{ h^2 = b^2 + p^2}}}[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
For triangle ( a )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex]
[tex] :\implies\qquad \sf{ h= \sqrt{144 + 324}}[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{468}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}}[/tex]
For triangle ( b )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{h =\sqrt{b^2 + p^2} }[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{(90)^2+(120)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{8100+14400}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{22500}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} }[/tex]
For triangle ( c )[tex] :\implies\qquad \sf{h^2 = b^2 + p^2 }[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{(100)^2)+(50)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{10000+2500}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{12500}}[/tex]
[tex] :\implies\qquad \underline{\underline{\pmb{\sf{h = 111.80mm}}} }[/tex]
Hypotenuse of triangle ( a ) = 21.63 mm
Hypotenuse of triangle ( b ) = 150 mm
Hypotenuse of triangle ( c ) = 111.80 mm
Explanation :find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
[tex]h^2 = b^2 + p^2[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
[tex]For \: \: triangle ( a )
\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex]\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex][tex]\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex][tex]\qquad\sf{h=\sqrt{ (12)^2 + (18)^2 }} \\ \\ \qquad \sf{ h= \sqrt{144 + 324}} \\ \\ \qquad \sf{ h = \sqrt{468}}
\\ \\\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}} \\ \\ For \: \: triangle ( b ) \qquad \sf{ h^2 = b^2 + p^2} \\ \\ \qquad \sf{h =\sqrt{b^2 + p^2} } \\ \\ \qquad \sf{ h = \sqrt{(90)^2+(120)^2}} \\ \\ \qquad \sf{ h=\sqrt{8100+14400}} \\ \\
\qquad \sf{ h =\sqrt{22500}} \\ \\\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} } \\ \\ For \: \: triangle ( c ) \qquad \sf{h^2 = b^2 + p^2 } \\ \\ \qquad \sf{ h=\sqrt{b^2 + p^2}} \\ \\\qquad\sf{ h=\sqrt{(100)^2)+(50)^2}} \\ \\\qquad\sf{ h=\sqrt{10000+2500}} \\ \\ \qquad \sf{ h =\sqrt{12500}} \\ \\
\qquad\underline{\underline{\pmb{\sf{h = 111.80mm}}} } [/tex]
Related Questions
Sydney read 50 pages in 40 minutes. She reads at a constant rate.
How many pages can Sydney read per minute
Answers
Answer:
divide the number of pages by the time
Step-by-step explanation:
=50/40
=5/4
= 1.25/per minute
solve for x and round if necessary
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \sin(37 \degree) = \frac{0.6}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \frac{3}{5} = \frac{0.6}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = 5 \times 0.6[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \div 3[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 1[/tex]
Therefore, the required value of x is 1
Answer:
[tex]\displaystyle 1[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{0,6} = csc\:37 \hookrightarrow 0,6csc\:37 = x \hookrightarrow 0,9969840846... = x \\ \\ 1 ≈ x[/tex]
OR
[tex]\displaystyle \frac{0,6}{x} = sin\:37 \hookrightarrow xsin\:37 = 0,6 \hookrightarrow \frac{0,6}{sin\:37} = x \hookrightarrow 0,9969840846... = x \\ \\ 1 ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
!!!!!!!!!!!!!!!!!!!!!!!!!HELP!!!!!!!!!!!!!!! Find the slope of the line.
Answers
Answer:
3/1
Step-by-step explanation:
Make sure you know a few concepts first:
The point where the line crosses the y-axis (or vertical axis) is called the y-intercept.Slope is commonly taught using [tex]\frac{rise}{run}[/tex] as I will teach it here.First, find the y-intercept of the line. This line crosses the y-axis as (0,0), so that is the y -intercept.Find another point on the line, preferably where it crosses a whole-number coordinate (just for simplicity… you can use any point on the line). We will use the point (1,3). Counting in your head, count vertically from (0,0) until you are horizontal to the point (1,3) we chose earlier. Put the distance it took to reach that point on the top (numerator) of the fraction. Because it takes 3 counts to be horizontal, your fraction should look like [tex]\frac{3}{run}[/tex].Count horizontally until you reach the point (1,3). Put the number of units on the bottom (denominator) of the fraction. The number was 1 unit, so your finished fraction which is the slope is [tex]\frac{3}{1}[/tex].Alternatively
Use the formula for slope from two points… [tex]\frac{x_{1} -y_1}{x_2-x_1}[/tex]Find two points on the line. We will use (0,0) and (1,3). Designate one point as 1 and the other as 2. We will choose (0,0) to be 1 and (1,3) to be 2.Plug in the points following the “key” you created: Let x₁ be the x coordinate from ordered pair 1, let y₁ be the y coordinate point from ordered pair 1, etc. Following this pattern, you should be set up like this: [tex]\frac{3-0}{1-0}[/tex]Subtract to get [tex]\frac{3}{1}[/tex] as your slope.Carlos vende vasos con 250 ml de limonada cada uno. si preparó 9 litros de limonada, ¿cuántos vasos de limonada puede servir?
Answers
En cada litro hay 4 vasos
9x4= 36
pls help i will give 5 starts and brainliest question is down below 9:22
Answers
4) -0.3 = -1/3 < -1/7 since the bigger a negative number is the less positive it is. 1/8 is positive so it is clear that it should be placed last. & thus do all options this way.
5) B
Area of a triangle = ½ bh.
where b = base &
h = height.
Area of outer shape = (½ x 16 x 12) in^2.
= 96 in^2.
Area of unshaded inner shape = (½ x 3 x 4) in^2.
= 6 in^2.
Area of shaded region = (96 – 6) in^2.
= 90 in^2.
No links just the Answer please!!!
Answers
Answer:Its -3.5
Step-by-step explanation:
Find the length of the wire
Answers
Answer:
Step-by-step explanation:
It could be 32m. Maybe, I'm not positive though.
Answer:
Hope you like the answer
Step-by-step explanation:
Mark me as Brilliant if you like the answer
1. D=5.9 ft.
calculate the circumference of the circle.
2. D=3.2 ft.
calculate the circumference of the circle.
3. D= 6.1 ft.
calculate the circumference of the circle.
4. R= 3.7 m.
Calculate the circumference of the circle.
5. R=6.2
Calculate the circumference of the circle.
6. R=5.1 Ft.
Calculate the circumference of the circle.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
As we know, we can calculate the circumference of a circle in terms of its diameter as :
[tex]\qquad \sf \dashrightarrow \:c = \pi d[/tex]
where, c = circumference and d = diameter
And also, circumference of circle is terms of radius (r) is :
[tex]\qquad \sf \dashrightarrow \:c = 2\pi r[/tex]
Now, let's move on to questions ~
First[tex]\qquad \sf \dashrightarrow \:3.14 \times 5.9 [/tex]
[tex]\qquad \sf \dashrightarrow \: \approx18.53 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Second[tex]\qquad \sf \dashrightarrow \:3.14 \times 3.2[/tex][tex] \qquad \sf \dashrightarrow \: \approx10.048 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Third[tex]\qquad \sf \dashrightarrow \:3.14 \times 6.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx19.15 \: ft[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fourth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 3.7[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×11.62 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx23.24 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Fifth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 6.2[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2× 19.47 \: units[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx38.94 \: m[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
Sixth[tex]\qquad \sf \dashrightarrow \:2×3.14 \times 5.1[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx2×16.01 \: ft[/tex]
[tex]\qquad \sf \dashrightarrow \: \approx \: 32.02m[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
pls help i need this FASTTTT
Answers
Answer:
31 cm2
Step-by-step explanation:
Rectangle 5X2 = 10 cm2
Triangle (6)(7)/2 = 42/2 = 21 cm2
Total area = 10 + 21 = 31 cm2
Hope this helps
31 cm^
Explanation:
We break it down by finding the areas of individual shapes first then add them together.
What is the length of the sides of kite abcd? ab = 20; cd = 15 ab = 15; cd = 20 ab = 9; cd = 16 ab = 24; cd = 25
Answers
The length of the side AB and side CD of kite abcd which is shown in the figure is 15 units and 20 units respectively.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
Let the intersection point of dignoals is O. The figure of the kite ABCD, is attached below. The sides of the kite ABCD, are,
[tex]AO=12\\OB=9\\CO=12\\OD=16[/tex]
In the triangle AOB using the pythagours theorem,
[tex]AB=\sqrt{(AO)^2+(OB)^2}\\AB=\sqrt{(12)^2+(9)^2}\\AB=\sqrt{225}\\AB=15[/tex]
Similarly, in the triangle DOC using the pythagours theorem,
[tex]CD=\sqrt{(CO)^2+(OD)^2}\\CD=\sqrt{(12)^2+(16)^2}\\CD=\sqrt{400}\\CD=20[/tex]
Thus, the length of the side AB and side CD of kite abcd which is shown in the figure is 15 units and 20 units respectively.
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Answer:
its B
Step-by-step explanation:
What is the answer to this question????
Answers
Answer:
Yes, its a linear function
Step-by-step explanation:
See, all the results here are one-one which means for a distinct input there will be a distinct output.
That's why its a linear function
Find the missing dimension of the cone.
Volume = 118π ft3
2/3 ft
h =_ft
Answers
The height of the cone with a volume of 1/18π ft³ is: 1.5 ft.
What is the Volume of a Cone?Volume of a cone = 1/3πr²h, where, h = height of cone, and r = radius of the cone.
Given the following:
Volume = 1/18 π ft³Diameter = 2/3 ftRadius = (2/3)/2 = 1/3 ftHeight (h) = ?Plug in the values into the volume formula:
1/18π = 1/3π(1/3)²h
1/18π = 1/3π(1/9)h
1/18π = (πh)/27
Divide both sides by π
1/18 = h/27
Cross multiply
27 = 18h
27/18 = h
h = 1.5
Therefore, the height of the cone with a volume of 1/18π ft³ is: 1.5 ft.
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https://brainly.com/question/13677400
The balloon rises vertically so that the distance between the balloon and Student A is 90 feet. How
many feet did the balloon rise? Express your answer to the nearest foot.
Answers
Using the Pythagorean Theorem, it is found that the balloon rises 67.08 feet.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Researching this problem on the internet, it is found that the situation is modeled by a right triangle, in which the horizontal distance between the balloon and the student is of 60 ft, the vertical distance is of h, while the hypotenuse is of 90 ft, hence:
[tex]60^2 + h^2 = 90^2[/tex]
[tex]h = \sqrt{90^2 - 60^2}[/tex]
[tex]h = 67.08[/tex]
The balloon rises 67.08 feet.
More can be learned about the Pythagorean Theoremat https://brainly.com/question/26396675
where can u buy a ruler that is 3 feet long
Answers
Answer:
A yard sale.
Step-by-step explanation:
lol
What is this question really about? Could you perhaps dive a little bit more into detail please? Ty
(100 POINTS !!) Identify the vertex of the parabola.
Answers
Answer:
(-4,0)
Step-by-step explanation:
Part A
The maximum angle of elevation for a ramp designed to be safe for a motorized wheelchair is 7.1°.
Is the ramp at the local library safe for motorized wheelchairs? Explain your answer.
Answers
Answer: Not safe
Step-by-step explanation:
Let the angle of elevation of the ramp be θ, then:
[tex]\begin{aligned}&\sin \theta=\frac{1.5}{10}=0.15 \\&\theta=\sin ^{-1}(0.15) \approx 8.63^{\circ}\end{aligned}[/tex]
But the maximum angle for the ramp cannot exceed 7.1°. The calculated angle of elevation will make it difficult, if not impossible, for motorized wheelchairs to get up the ramp.
Therefore, the ramp at the local library is not safe for motorized wheelchairs
Find the volume of the cylinder. round to the nearest tenth.
Answers
Answer:
3217.00
Step-by-step explanation:
V=πr^2h=π·8^2·16≈3216.99088
Answer:
804.2 or 803.8
Step-by-step explanation:
volume = π · r2 · h
π · [tex]4^{2}[/tex] · 16 = 804.2
3.14 · [tex]4^{2}[/tex] · 16 = 803.8
Brianna started watching a movie at 2:45 p.m. If the movie is 2 hours and 32 minutes long, when will it be over?
Answers
Answer:
It will be over at 5:17 pm
Step-by-step explanation:
2:45 +32 would be 3:17, we add 2 hours it would be 5:17
Answer:
5:17 pm
Step-by-step explanation:
Since Brianna started watching a movie at 2:45 p.m and the movie is 2 hours and 32 minutes long
Thus,
2:45 + 2 and 32 Minutes
2 + 2 = 4
45 + 32 = 77 minutes
1 Hour = 60 Minutes
Thus, 77 - 60 =17
Hence, 4 + 1 = 5
Thus, the movie will be over at 5:17 Pm
~Lenvy~
3. What is the area of the triangle below?
6.0 ft^2
8.6 ft^2
15.0 ft^2
17.2 ft^2
Answers
Answer:
6.0 ft^2
Step-by-step explanation:
hope this helps
Theo is a cleaner,
The table shows information about the time it will take him to clean
each of four rooms in a house,
Theo wants to clean all four rooms
Room
Time
in one day
Kitchen 1 hour 50 minutes
He will have breaks for a total time
of 85 minutes,
Lounge 55 minutes
Theo is going to start cleaning at 9 am,
Bedroom 1 1/2 hours
What time will he finish cleaning?
Bathroom
35 minutes
Answers
Step-by-step explanation:
1 hour 50 minutes = 110 mins
1 1/2 hours = 90 mins
add all these:
110
90
85
55
35
when you add all these you get 375
every hour has 60 minutes
375 ÷ 60 = 6.15
if he starts at 9 am and he cleans for 6.15 hours he will be finished by 3:15pm.
Based on the number of minutes Theo will take to clean the various rooms, and the time he will take to rest, he will finish cleaning at 3:15 pm.
What time will Theo finish cleaning?The best thing to do here is to convert all the minutes to decimals. This would make adding them up easier.
Kitchen = 1 hour 50 minutes = 1 + 50/60 = 1.833 hours
Lounge = 55 minutes = 55/60 = 0.916 hours
Bedroom = 1.5 hours
Bathroom = 35 minutes = 35/60 = 0.583
Breaks = 85 / 60 = 1.417
Add them up:
= 1.833 + 0.916 + 1.5 + 0.583 + 1.417
= 6.249 hours
= 6 + (0.249 x 60 minutes)
= 6 hours 15 minutes
The time he will finish is:
= 6 hours 15 + 9
= 1515 hours
= 3:15 pm
Find out more on operations involving time at https://brainly.com/question/1040096.
What is the value of x? E Enter your answer in the box.
Answers
Step-by-step explanation:
Right away i notice the 45° angle and the 90° angle in triangle RTQ, this means that the remaining angle must be 180-(90+45)=45°.
If it isn't obvious yet, triangle RTQ is a right isosceles triangle where RT=RQ=x.
Now looking at my other triangle RST
I know that RT=x, RS=2√3 and ST is unknown.
So i cannot apply my Pythagorean theorm.
HOWEVER i do notice 60 degree angle and the 90 degree angle, which means that the last angle must be 180-(90+60)=30° and this triangle (RST) must be a half equilateral triangle;,
Now i can use the relation which describes the relation between the hypotenuse(x) and the side opposite or facing the 60° angle (RS=2√3).
RS=x√3/2
2RS=x√3
2×2√3=x√3
4√3=x√3
4√3/√3=x
x=4 :P
I think of a number. I multiply it by 5. I then subtract 19. Finally, I double the resu The final number is 22. What number did think of?
Answers
Answer:
8.2 is your answer.
Step-by-step explanation:
first you would add 22 and 19 together to get 41
then you divide by 5 to get your answer 8.2
22+19=41÷5=8.2
Hello people ~
If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11° (c) 79° (d) 101°
Answers
Hey there!
Complementary angles add up to 90 degrees.
We are given
An angle of 79 degrees
and we're asked to find the complement of the angle.
So let's set up an equation:
79+x=90
where x=the unknown angle
Subtract 79 from both sides:
79-79+x=90-79
x=11
Hence, the measure of the unknown angle is
[tex]\boxed{\boxed{\bold{11}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#LearningIsFun
[tex]\rule{200}{2}[/tex]
(b) 11°
The sum of two angles is equal to 90 degrees.
Here, one angle is 79°
let the other angle be xsteps:
x + 79° = 90°x = 90° - 79°x = 11°3 3/5 + 1 1/6 answer as a fraction
Answers
Answer:
[tex]\boxed{\sf{4\dfrac{23}{30} }}[/tex]Step-by-step explanation:
It is necessary to add the whole numbers of fractions from left to right in order to solve this problem.
3 3/5+1 1/6First, you have to add the whole numbers.
3+1=4
After that, you can combine by a fraction.
6*3=18
18/5+ 1 1/6
1+6=7
7/6
Rewrite the problem down.
18/5+7/6
Solve.
5*6=30
143/30
=23/30
[tex]\boxed{\sf{4\dfrac{23}{30} }}[/tex]
Therefore, the final answer is 4 23/30.I hope this helps you! Let me know if my answer is wrong or not.
Analyze the diagram below and answer the question that follows.
In the triangle above, what is the measure of ∠A?
A. m∠A = 30°
B. m∠A = 45°
C. m∠A = 60°
D. cannot be determined
Answers
Answer:
B
Step-by-step explanation:
sames sides same angle
180=90+2x
180-90=2x
90=2x
x=45
omly
Purple
Green
Blue
in
Number
6
9
5
of trials
Based on the data, how many times
would you expect Anya to pick a
purple marble if she ran 90 trials?
Answers
90 / 10
= 9
Answer 9
help guys with this question
Answers
Answer:
slope: 2
points: (2, 4), (6, 12)slope:
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{12-4}{6-2}[/tex]
[tex]\rightarrow \sf \dfrac{8}{4}[/tex]
[tex]\rightarrow 2[/tex]
Hi please help me me with this thank you so much
Answers
⇒ Area = 18 * 18 = 324 square inches
Question 2: Height of PyramidHeight of Pyramid: distance between the tip of the figure to the base
⇒ Height = 14 inches
Question 3: Volume of PyramidVolume of Pyramid's formula ⇒ 1/3 * (base area) * height
⇒ [tex]\frac{1}{3} * 324 * 14 = 108 * 14 =[/tex] 1512 cubic inches
Hope that helps!
how do I multiply 6ab (xa+ya^6 +8)
Answers
Answer:
6xba^2 + 6yba^7 + 48ab
Step-by-step explanation:
To do this, you have to multiply 6ab by each of the inside terms,
So you can write it out like this
6ab (xa + ya^6 + 8)
6ab(xa) + 6ab(ya^6) + 6ab(8)
Then you can simplify:
6xba^2 + 6yba^7 + 48ab
(When you multiply the same variable by itself, you turn it into an exponent)
For example x * x = x^2
Or x^4 * x^3 = x^7
Find the length of the darkened arc. leave your answer in terms of
Answers
Answer:
a
Step-by-step explanation:
you can split nine into three
Answer:
The answer is A.
Step-by-step explanation:
You gotta split 9 into 3